Semiclassical instability of dynamical warp drives (0904.0141v2)

Abstract: Warp drives are very interesting configurations in General Relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein's equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of Quantum Inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical back-reaction.

• The paper demonstrates that semiclassical backreaction produces a thermal flux analogous to Hawking radiation at the warp bubble horizons.
• It uses renormalized stress-energy tensor analysis to reveal exponentially growing instabilities at the front wall of superluminal warp drives.
• The research indicates that, despite being valid solutions in general relativity, warp drives are practically unfeasible due to quantum-induced instabilities and exotic matter requirements.

Semiclassical Instability of Dynamical Warp Drives: An Analysis

This paper investigates the semiclassical stability of warp-drive spacetime geometries within the context of general relativity (GR) and quantum field theory. Warp drives, as proposed by Alcubierre, have generated considerable interest due to their theoretical potential for superluminal (faster than light) travel, which is achieved through a bubble of spacetime that manipulates the surrounding gravitational field. These warp drives require the existence of exotic matter, which violates known energy conditions, making their feasibility highly speculative.

Key Findings

1. Causal Structure and Metric Analysis: The paper examines the causal structures of both eternal and dynamically created warp drives. The geometries of these warp-drive bubbles are analyzed using a version of the Alcubierre metric, with a focus on regions of spacetime that exhibit characteristics akin to black and white horizons.
2. Renormalized Stress-Energy Tensor (RSET): A critical aspect of the research is the paper of the RSET of a quantum field within the warp-drive geometries. The analysis reveals that similar to black hole spacetimes, the warp drive's spacetime can produce a thermal flux of particles, analogous to Hawking radiation, which is observed by an internal observer as originating at the warp bubble's horizons.
3. Semiclassical Instabilities: A significant conclusion from the RSET analysis is that superluminal warp drives are fundamentally unstable due to semiclassical backreaction effects. The stress-energy tensor is shown to increase exponentially in the vicinity of the warp bubble's front wall, indicating an instability that could prevent the warp drive from sustaining superluminal speeds for any practical duration.

Theoretical and Practical Implications

• Theoretical Implications: The theoretical underpinning of warp drives challenges our current understanding of GR and quantum field theory. The paper highlights that while warp drives are mathematically valid solutions under GR, the quantum corrections indicate that such constructs are not physically viable due to instabilities.
• Practical Implications: If such a warp drive were to be realized, the high temperatures of induced Hawking radiation and significant energy requirements, based on the violation of quantum inequalities (QI), make these constructs practically infeasible with our current technology and understanding of physics.

Future Directions

Future research may investigate alternative ways to circumvent these instabilities, potentially by exploring new physics beyond our current quantum field theory framework, including ideas involving modified dispersion relations or analog models of spacetime. The challenge remains to find a configuration that is quantum mechanically stable and does not require impractical amounts of exotic matter.

In summary, while the concept of a warp drive remains a fascinating theoretical exploration, this paper presents robust arguments that current warp-drive solutions are not viable when accounting for semiclassical effects. This analysis underscores the persistent challenges and boundaries of merging GR with quantum mechanics, particularly in scenarios that involve exotic spacetime geometries. The work provides a foundation for both ongoing theoretical inquiries and a better understanding of the limitations imposed by quantum field effects on gravitational constructs.